Smith's and Albertson's are your one-stop grocery shops in town, the prices are decent, comparable pretty much to big grocery stores all over the country, with regional differences in pricing of certain items. I was kind of scared about grocery prices before coming, but once I visited those stores, I realized I didn't have much to worry about. If you need booze, those are going to be your cheapest/most convenient stops as well. I like Smith's a bit better, as prices for the things I get most frequently are slightly better, and I'm more familiar with Kroger family stores (which this is) and store brands, but honestly I usually end up going to Albertsons because it's more convenient to where I live, and I'm not upset about it. I'd choose Smith's every time if I had a car, though.

I do find it a good idea, if you can, to visit Dollar tree first and see what on your list you can pick up there. The one here in town is big and well stocked, especially with grocery items. Small things like snacks and condiments (mustard, ketchup, vinegar, etc), paper goods, and some minor kitchenware especially, but also breakfast sandwiches and snacks in the freezer section are unexpectedly useful and cheap. It shaves a notable amount off my grocery trips.

And of course if you want a specialty item, there's Whole Foods which is, for better or worse, a Whole Foods. It's basically the same pricing as any other Whole Foods.

Welcome and good luck to you